Base field 6.6.1229312.1
Generator \(w\), with minimal polynomial \(x^{6} - 10x^{4} + 24x^{2} - 8\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[392, 14, -\frac{1}{2}w^{3} + 4w]$ |
| Dimension: | $1$ |
| CM: | yes |
| Base change: | yes |
| Newspace dimension: | $193$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + 2w^{3} + 2w^{2} - 3w - 3]$ | $\phantom{-}1$ |
| 7 | $[7, 7, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + 2w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}1$ |
| 8 | $[8, 2, -\frac{1}{4}w^{5} + 2w^{3} - 3w]$ | $-1$ |
| 41 | $[41, 41, -\frac{1}{4}w^{4} - \frac{1}{2}w^{3} + \frac{3}{2}w^{2} + 3w - 1]$ | $\phantom{-}6$ |
| 41 | $[41, 41, -\frac{1}{2}w^{2} - w + 2]$ | $\phantom{-}6$ |
| 41 | $[41, 41, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + 2w^{2} - 5w - 2]$ | $\phantom{-}6$ |
| 41 | $[41, 41, \frac{1}{4}w^{5} - \frac{1}{4}w^{4} - \frac{5}{2}w^{3} + 2w^{2} + 5w - 2]$ | $\phantom{-}6$ |
| 41 | $[41, 41, \frac{1}{2}w^{2} - w - 2]$ | $\phantom{-}6$ |
| 41 | $[41, 41, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + \frac{3}{2}w^{2} - 3w - 1]$ | $\phantom{-}6$ |
| 71 | $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + w^{2} - 5w + 1]$ | $\phantom{-}0$ |
| 71 | $[71, 71, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + \frac{5}{2}w^{3} + \frac{3}{2}w^{2} - 6w - 2]$ | $\phantom{-}0$ |
| 71 | $[71, 71, \frac{1}{4}w^{4} - \frac{1}{2}w^{3} - \frac{5}{2}w^{2} + 3w + 4]$ | $\phantom{-}0$ |
| 71 | $[71, 71, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - \frac{5}{2}w^{2} - 3w + 4]$ | $\phantom{-}0$ |
| 71 | $[71, 71, \frac{1}{2}w^{4} - \frac{7}{2}w^{2} + w + 3]$ | $\phantom{-}0$ |
| 71 | $[71, 71, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + \frac{5}{2}w^{3} - w^{2} - 5w - 1]$ | $\phantom{-}0$ |
| 97 | $[97, 97, \frac{1}{4}w^{5} - \frac{5}{2}w^{3} - \frac{1}{2}w^{2} + 5w]$ | $-10$ |
| 97 | $[97, 97, -\frac{1}{4}w^{4} + \frac{3}{2}w^{2} + w + 1]$ | $-10$ |
| 97 | $[97, 97, -\frac{1}{4}w^{4} + \frac{1}{2}w^{3} + 2w^{2} - 3w - 4]$ | $-10$ |
| 97 | $[97, 97, \frac{1}{4}w^{4} + \frac{1}{2}w^{3} - 2w^{2} - 3w + 4]$ | $-10$ |
| 97 | $[97, 97, \frac{1}{4}w^{4} - \frac{3}{2}w^{2} + w - 1]$ | $-10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -\frac{1}{4}w^{5} - \frac{1}{4}w^{4} + 2w^{3} + 2w^{2} - 3w - 3]$ | $-1$ |
| $7$ | $[7, 7, -\frac{1}{4}w^{5} + \frac{1}{4}w^{4} + 2w^{3} - 2w^{2} - 3w + 3]$ | $-1$ |
| $8$ | $[8, 2, -\frac{1}{4}w^{5} + 2w^{3} - 3w]$ | $1$ |